Fix differential equation tutorial

[devmotion]

I've wanted to do this for quite some time but unfortunately my computer broke while working on an update...

So here are some fixes for the differential equation tutorial.

Most notably,

• it fixes the MvNormal deprecations
• fixes the trajectories of posterior samples (the used the wrong parameters)
• it uses more "modern" and simpler SciML syntax
• specifies the solver for the DDE example correctly.

Preview: https://julialang-buildkite-artifacts.s3.amazonaws.com/turingtutorials/e3c8bc002f5223b50eb6e9c7902473c040159c0aa4d5942d979166fa05bcb422/html/10-bayesian-differential-equations/10_bayesian-differential-equations.html

[devmotion]

@staticfloat I think there might be an issue with coppermind? https://buildkite.com/julialang/turingtutorials/builds/76#9b6b2925-254f-43b2-8401-9a7224be6376/205-207

[devmotion]

@staticfloat It seems it's a problem specifically with aarch64 (or the workers) as it still works with x86_64: https://buildkite.com/julialang/turingtutorials/builds/78#b12d7990-0ba6-422b-9a30-df85278cc46d Probably bash does not support all features in the failing builds? The offending line seems to be https://github.com/staticfloat/coppermind-buildkite-plugin/blob/bc1c8b1f473651490bcaed15dfe16488d447a0e4/hooks/pre-command#L8.

[devmotion]

Ah no, it's just the exit code. So I assume bash might not be available and/or installed properly?

[devmotion]

Will be fixed by #298.

[yebai]

Maybe add a link to the docs on how to change AD backends here?

[devmotion]

It's shown how to change it (and change it back) below, is that sufficiently clear? Or should we add a link here? Or maybe rather below?

[yebai]

thanks for the clarification, that should be sufficient.

[devmotion]

There's one remaining issue, namely that pool_chain is not exported by MCMCChains. It's a hack anyway, so I think I'll just go and fix TuringLang/MCMCChains.jl#223. Then pool_chain is not needed anymore and the code becomes simpler.